-x2 - 4x + 21
Factorise

9514 1404 393

  -(x -3)(x +7)

Step-by-step explanation:

Apparently, you're supposed to match the given expression with the parts of the identity ...

  (x + a)(x + b) = x² +(a +b) +ab

First of all, we notice that the sign of x² in our given expression is negative. So, we factor -1 out of the expression first.

  -x² -4x +21 = -(x² +4x -21)

Now, matching the coefficients of x, and the constant to those in our identity, we see ...

  a + b = 4 . . . . . coefficients of x

  ab = -21 . . . . . . constants

It is relatively easy to find the factors of -21. We are interested in those factor pairs such that the sum is positive:

  -21 = -1(21) = -3(7) = -7(3) . . . . at this point the sum -7+3 becomes negative

The factor pair a=-3, b=7 will satisfy ...

  a + b = -3 + 7 = 4

  ab = (-3)(7) = -21

So, our factorization is ...

  -x² -4x +21 = -(x² +4x -21) = -(x -3)(x +7)

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step-by-step explanation:

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step-by-step explanation:

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